An inverse problem in an elastic domain with a crack : a fictitious domain approach

An inverse problem applied to volcanology is studied. It consists in the determination of the variable pressure applied to a crack in order to fit observed ground displacements. The deformation of the volcano is assumed to be governed by linear elasticity. The direct problem is solved via a fictitio...

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Bibliographic Details
Published inComputational geosciences Vol. 26; no. 2; pp. 423 - 435
Main Authors Bodart, Oliver, Cayol, Valérie, Dabaghi, Farshid, Koko, Jonas
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.04.2022
Springer Verlag
Subjects
Earth and Environmental Science
Earth Sciences
Geotechnical Engineering & Applied Earth Sciences
Hydrogeology
Mathematical Modeling and Industrial Mathematics
Original Paper
Sciences of the Universe
Soil Science & Conservation
Volcanology
Conjugate gradient
Fictitious domain
Linear elasticity
Inverse problem
Crack
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Summary:An inverse problem applied to volcanology is studied. It consists in the determination of the variable pressure applied to a crack in order to fit observed ground displacements. The deformation of the volcano is assumed to be governed by linear elasticity. The direct problem is solved via a fictitious domain method, using a finite element discretization of XFEM type. The ground misfit is minimized using a combination of a domain decomposition and optimatily conditions. The gradient of the cost function is derived from a sensitivity analysis. Discretization of the problem is studied. Numerical tests (in 2D and 3D) are presented to illustrate the effectiveness of the proposed approach. In particular, we find that a quasi-Newton method is more efficient than a conjugate gradient method for solving the optimization problem.
ISSN:1420-0597
1573-1499
DOI:10.1007/s10596-021-10121-7